Using speech-like sounds or a modification of speech
something, but which is not part of the language
Mood indicators like whispering and shouting are paralinguistic. But not all forms of emphasis are outside the language system like that: contrastive stress and question intonation are grammatical in nature, as in: This is the one. Is this the one?
The clicking written as tsk, the release of breath written whew or phew, and the brrr of cold are paralinguistic. They aren't used as part of sentences, in contrast to other exclamations such as oh!, and they don't use normal speech-sounds of English. We would normally report them with the word 'go' rather than 'say': John said 'Oh!', but John went tsk tsk.
None of these tests is definitive and I don't think we would want to draw a firm line between the linguistic and paralinguistic. A lot of exclamations have conventionalized forms, where we say them as words: whee, ouch, aargh. These can probably be considered as inside the language, but with a peculiarly limited status. Related to this is onomatopoeia, which is basically linguistic, not paralinguistic: we say the word 'bang' or 'cock-a-doodle-do', we don't make a banging or cock-crow noise.
Paralinguistic effects can be applied to ordinary individual words: for example the drawn-out and lowered timbre on emphatic so often written something like sooo, or Samantha's yowling Well? in Bewitched.
The mouth sounds we use paralinguistically might or might not be possible sounds in a language. The alevolar click tsk and the bilabial roll brr are a normal part of words in a few languages. A sigh, or an insulted hmph! aren't in any. Vocal effects like creaky voice are a normal property of individual vowels in some languages, whereas English only uses it paralinguistically: for example in the resigned, reluctant 'Yes, I'll do it now'. In Received Pronunciation creak is used more than in other accents, some of it as speaker's voice quality but partly also to give an effect of hesitation.
Although some effects like shouting and whispering must be universal among humans, many paralinguistic effects are very culturally specific. Don't expect a sing-song intonation to be used for mockery to work in other cultures. (In fact I have no idea how common this is.) The Mayan language Tzeltal use creaky voice for complaints and commiserations, and falsetto for polite greetings and formal conversation.
The paralinguistic is intentionally communicative. It is to be distinguished from the extralinguistic possibilities of mouth noises (such as teeth chattering) and speech, such as the features individual to speakers that make them sound old or young, female or male, bunged-up or hoarse. People often vary idiosyncratically in how much they use features such as nasalization. These personal characteristics are usually part of the higher formants of the speech signal, and play no role in the meaning of the sounds. Some sounds may be extralinguistic when involuntary but available for use as paralanguage, such as a sigh.
Tzeltal from: Laver, 1994, Principles of phonetics, Cambridge